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e 8 If yz-1, show that:-1 |
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Answer» (1 + x + y^-1)-1+(1 + y + z-1)-1+ (1 + z + x-1)-1= (1 + x + 1/y)-1+(1 + y + 1/z)-1+ (1 + z + 1/x)-1= (1 + x + xz)-1+(1 + y + 1/z)-1+ (1 + z + 1/x)-1[xyz = 1, or xz = 1/y]= (1 + x + xz)-1+{(z + yz + 1)/z}-1+ {(x + xz + 1)/x}-1= (1 + x + xz)-1+{(z + 1/x + 1)/z}-1+ {(x + xz + 1)/x}-1[xyz = 1, or yz = 1/x]= (1 + x + xz)-1+{(xz + 1 + x)/xz}-1+ {(x + xz + 1)/x}-1= 1 / (1 + x + xz) + xz / (1 + x + xz) + x / (x + xz + 1)= (1 + xz + x) / (1 + x + xz)= 1 |
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